The control properties of small eye movements

THE CONTROL PROPERTIES

OF SMALL EYE MOVEMENTS

THE CONTROL PROPERTIES

OF SAAALL EYE MOVEMENTS

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Proefschrift

Ter verkrijging van de graad van

doctor in de technische wetenschappen

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus

prof. dr. J.M. Dirken,

in het openbaar te verdedigen

ten overstaan van het College van Dekanen

op donderdag 27 november te 16.00 uur

door JOHANNES DE BIE

geboren te Langbroek

natuurkundig ingenieur

Omslag: Herre Methorst

TR diss ^

1 5 1 3

Dit proefschrift is goedgekeurd door de promotoren

prof. dr. G. van den Brink en prof. dr. ir. F.A. Bilsen

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Ogen, die in mij rusten, ben ik doel.

Aan het onderbewuste onttrekken zij de resten ziel en gevoel,

opdat zich gans en al de leden zullen sluiten. Maar ik kan nog niet buiten dit laatst voedsel

voor vers en wil.

Gerrit Achterberg

TABLE OF CONTENTS

Chapter 1 INTRODUCTION 9

Chapter 2 REVIEW OF THE LITERATURE 13

2.1 Introduction 13 2.2 The saccadic system 13

2.3 The smooth pursuit system 16 2.4 Fixation of a stationary target 22

Chapter 3 METHODS 29

3.1 Introduction 29 3.2 Eye movement recording with a coil in a magnetic field 30

3.3 The field uniformity 31 3.4 Accuracy of the eye movement recording 3 5

3.4.1 Introduction 35 3.4.2 Method 37 3.4.3 Results 40 3.5 Stimuli, subjects and experimental procedures . . . 41

Chapter 4 GENERAL FIXATION CHARACTERISTICS 45

4.1 Individual patterns 45 4.2 The average fixation point 52

4.3 The influence of the task on fixation 55

4.3.1 Introduction 55 4.3.2 Influence of task on general fixation

characteristics 56 4.3.3 Influence of task on saccade triggering . . . . 58

4.4 Influence of fixation target symmetry 60

4.4.1 Introduction 60 4.4.2 Method 61 4.4.3 Results 61 4.4.4 Discussion 66

-5-Chapter 5 THE SLOW CONTROL SYSTEM 69

5.1 Introduction 69 5.2 Methods 71 5.3 Step reactions vs. fixation 72

5.3.1 Method 72 5.3.2 Results 74 5.4 Stabilized step response 74

5.4.1 Method 74 5.4.2 Results 76 5.5 Normal step response 78

5.5.1 Method 78 5.5.2 Results 79 5.6 Step/ramp response 80 5.6.1 Method 80 5.6.2 Results 80 5.7 Discussion 82 5.7.1 Analysis 82 5.7.2 Model 84 5.7.3 Estimation of model parameters 87

5.7.4 Model results 92

Chapter 6 THE (MICRO)SACCADIC SYSTEM 98

6.1 Introduction 98 6.2 The corrective properties of microsaccades 99

6.3 The triggering of microsaccades . 103 6.3.1 Influence of small eye movements during

fixation 103 6.3.2 Influence of retinal error 105

6.3.3 Model for saccade triggering 108

6.4 Responses to larger steps 110 6.4.1 Introduction 110 6.4.2 Method 113 6.4.3 Results 113 6.4.4 Discussion 116 6.5 The cause of saccade variability 118

6.5.1 Introduction 118 6.5.2 Method 119 6.5.3 Results and conclusion 119

been measured first, roughly confirming the older literature. Then the important issue of why and how a (micro)saccade is triggered will be assessed in Section 6.3, and a simple model will be proposed to describe this process. Similar to the rela­ tionship between slow control and smooth pursuit, there is probably a connection between microsaccades during fixation and larger visually triggered saccades. One aspect of larger sac-cades will be treated in more detail in section 6.4, namely their consistent undershoot. Using particular stimulus condi­ tions and instructions to the subject, we increased the latency distribution of saccades in order to verify a hypothesis about the cause of that undershoot. Another theory providing a link between saccade undershoot and variability triggered us to per­ form the last experiment described in this thesis. In section 6.5 we try to find out what part of the saccade control loop gives the largest contribution to the saccade variability. Therefore, we compared the visual localization of a peripheral target with the saccade towards that target.

Several parts of this thesis have been published before. The afterimage Vernier method of measuring the accuracy of eye movement monitors (section 3.4) has been published in Vision Research (De Bie, 1985). In a short paper, the control function of microsaccades (section 6.2), their triggering (section 6.3) and a preliminary version of the slow control model (Chapter 5) have been described (De Bie and Van den Brink, 1984). The slow control model (Chapter 5) is covered in more detail in a second paper in Vision Research (De Bie and Van den Brink, 1986). The saccade undershoot, and its relationship to saccade and locali­ zation variability (sections 6.4 and 6.5) have been described in the edited proceedings of the Third European Conference on Eye Movements (De Bie et al., 1986).

and subjects completes Chapter 3.

C h a p t e r 4 d e a l s w i t h general fixation c h a r a c t e r i s t i c s . B e ­ fore the two m a i n types of eye movements are d i s c u s s e d , some general k n o w l e d g e is p r e s e n t e d . First of a l l , it must be clear w h e n fixation is 'normal'. Section 4.1 lists some c h a r a c t e r i s ­ tic types of fixational eye movements that can be encountered in d i f f e r e n t s u b j e c t s , b u t which fall o u t s i d e the 'normal' p a t ­ tern that has b e e n d e s c r i b e d in the l i t e r a t u r e . These 'irregu­ larities' occur o f t e n , and could provide some insight into the mechanism of fixation c o n t r o l . The m e m o r y , or 'time window' of the control system is necessary for the definition of a r e f e r ­ ence p o s i t i o n , at which the eye is considered to be on-target (section 4 . 2 ) . Since good fixation seems to b e of particular importance in tasks w h e r e a high visual acuity is needed, t h e r e l a t i o n s h i p between such a task and several p r o p e r t i e s of fix­ ational eye movements h a s been investigated. The results a r e presented in Section 4.3. In daily l i f e , a fixation target is usually selected from a complex s c e n e , w h i l e in laboratory c o n ­ d i t i o n s as a rule only one symmetric target is used. Section 4.4 d e s c r i b e s to what extent the average fixation position is influenced by nearby d i s t r a c t o r s .

After having established some general characteristics of f i x a t i o n , more a t t e n t i o n is given to the two s u b s y s t e m s , 'slow c o n t r o l ' and 'microsaccades'. The. slow control system is c o v ­ ered in Chapter 5. It will be shown that no d i f f e r e n c e s exist between slow control d u r i n g fixation and d u r i n g responses to small target m o v e m e n t s . That knowledge is used to establish an input-output r e l a t i o n s h i p for the slow control system, and to develop a model that is comparable with smooth pursuit m o d e l s from the l i t e r a t u r e . T h i s model has two parallel c h a n n e l s , a slow retinal e r r o r c h a n n e l , and a faster system that responds to the target v e l o c i t y . It w a s necessary to d e v e l o p a special stabilization t e c h n i q u e to separate the e f f e c t s of m i c r o s a c ­ cades and slow m o v e m e n t s . It will be shown that microsaccades have no influence on the slow control system.

S a c c a d e s form the subject of Chapter 6. Microsaccades d u r ­ ing fixation have been considered to be laboratory artefacts in recent l i t e r a t u r e , in contrast to older s t u d i e s , in which they w e r e looked at a s the m a i n instrument in correcting retinal e r ­ r o r s . The general c o n t r o l properties of these 'artefacts' h a v e

1 0

-Chapter 7 GENERAL CONCLUSIONS AND DISCUSSION 124

Appendix MAGNETIC FIELD CALCULATION 130

SUMMARY 13 4

SAMENVATTING 139

REFERENCES 14 5

CURRICULUM VITAE 156

-1. INTRODUCTION

The way in which our eyes move has interested scientists

through the ages. In this century, it became possible to meas­

ure eye movements quantitatively, thus providing the opportuni­

ty to correlate visual input with the eye movement output. The

apparent motionlessness of the eye when a stationary target is

being fixated is equally intriguing. It has become clear that

the minuscule motion of the eye that is still present during

fixation, a continuous slow movement, interrupted by abrupt

fast displacements - the microsaccades - greatly resembles the

two main types of larger eye movements. The role of both types

of fixational eye movements in keeping the eye 'on-target' as

well as their mutual relationship and that with larger eye

movements have not been fully established yet in the litera­

ture. Many of the studies in the past were descriptive in na­

ture, and did not provide a framework for further research,

causing our knowledge to be scattered. It is the purpose of

this thesis to quantify the input-output relationships of the

fixation control systems as much as possible, thereby providing

a basis for hypotheses and models that can be tested and fur­

ther developed.

In order to relate the present results to the current

knowledge, an extensive review of the literature is given in

Chapter 2. The review not only covers the fixational eye move­

ments, but also the smooth pursuit and saccade systems, since

the distinction commonly made between small and large eye move­

ments seems to be rather artificial. Furthermore, larger visu­

ally induced eye movements are much better quantified, and a

variety of models exists for the underlying control systems.

The tools for measuring eye movements are described in

Chapter 3. The method of a search coil in a magnetic field that

has been chosen by us is treated in more detail. In particular,

the usual method of generating a uniform field is critically

reconsidered. A new method has been developed to assess the ac­

curacy of the eye movement measurements of subjects while they

are wearing a search coil, using a combination of afterimages

and Vernier acuity. An explanation of the experimental proce­

dures and conditions as well as a description of the stimuli

2. REVIEW OF THE LITERATURE

2.1 Introduction

The human retina is not homogeneous. In a central area, the fovea, the receptors are more tightly packed, and visual acuity has a sharp peak (Polyak, 1941; Lie, 1980; Riggs, 1965). The fovea is also the area on which our attention is usually focussed. Eye movements play an essential role in getting and keeping the point of interest imaged on the fovea. They 'are brought about by three pairs of extra-ocular muscles: the in­ terior and exterior recti are for rotations in the horizontal plane, while the vertical rotations are caused mainly by the superior and inferior recti. However, the superior and inferior obliques are also necessary for pure vertical rotations. The last two pairs of eye muscles produce rotational movements as well, which are important in binocular vision and head movement compensations (Ditchburn, 1973 p. 2 1 ) . All muscles receive their input from the oculomotor neurons in the brain stem, which are involved in all types of eye movement (Keller, 1981)

On the basis of their appearance, the large eye movements can be divided into two classes: saccades, fast step-like dis­ placements of the eye, and slow continuous movements. This same distinction can be recognized in the eye movement literature, and will be made in'this review as well. Historically, fixation of a stationary target has always considered to be a special case, although the same types of eye movements are present dur­ ing fixation. That is why we will treat fixation separately in this chapter.

2.2 The saccadic system

In real life, saccades are used to move the image of a new object towards the fovea. They are very fast eye movements, having maximum velocities increasing with size up to 600 deg/ sec. The duration of a saccade depends on its size, from 30 ms for saccades smaller than 5 deg, up to 100 ms for 40 deg sac­ cades (Baloh et al., 1975). To initiate such a fast accelera­ tion, overcoming the viscous nature of the eye ball tissues, it

-13-is necessary for the eye muscles to apply a pulse-like force, followed by a step in order to keep the eye at its new position (Robinson, 1964). Anomalies in the relationship between the pulse and the step cause abnormal saccades, with either over­ shoot or undershoot followed by a slow drift to the new posi­ tion (glissade).

The burst of neural activity related to the saccadic pulse originates from burst cells in the pontine recticular formation in the brain stem. How this burst is controlled during the pro­ duction of a saccade of exactly the desired amplitude is not known. The most recent theory is the internal feedback theory, in which the actual eye position is continuously compared with the desired position, and the burst is stopped as soon as this is reached (Van Gisbergen and Robinson, 1977; Chun and Robin­ son, 1978; JÜrgens et al., 1981; Van Gisbergen et al., 1981). The input for the burst neurons comes mainly from two regions: the superior colliculus and the frontal eye fields. The differ­ ences between these two parallel pathways are not entirely clear. For an overview of the neurophysiology of saccades we refer to Robinson (1981) and Sparks (1986).

In normal life, the most saccades are made when we look around to explore the visual world, or in response to non-vis­ ual stimuli. In laboratory situations, there is usually one target that makes discrete steps, which the subject is instruc­ ted to follow. It appears that the following saccade is pro­ grammed in spatial, not in retinal coordinates; in other words, it brings the eye to a certain position in the orbit, independ­ ent of the original eye position. The saccade will be pro­ grammed correctly if, for instance, the eye is moved artifi­ cially between the triggering and execution of the saccade

(Mays and Sparks, 1980; Robinson, 1975). Normally, the latency of a saccade following a visual stimulus is about 0.2 sec. In a broad range, the saccade latency is independent of the size of the stimulus step, but it increases with very large (above 30

b deg) and very small steps (below 0.5 deg, Wyman et al., 1973 ) . A saccade is clearly triggered by the sudden appearance of a target in the periphery, but the mechanism is not completely understood. Activities in the fovea around the time of target appearance play an important role; it seems that the triggering of a saccade is facilitated by a short gap between foveal

tar-get offset and peripheral onset, and inhibited by an overlap (Reulen, 1984). Also, with predictable target positions, a spe­ cial type of short latency saccade occurs, called an express saccade (Boch and Fisher, 1984; Fisher and Ramsperger, 1984), in both man and monkey alike.

Most models óf the saccadic system assume different, usu­ ally sequential, mechanisms for the triggering of a saccade, and for the calculation of its amplitude (Hou and Fender, 1979; Komoda et al., 1973). Much about the amplitude calculation has been revealed by double spot and double step experiments. In double spot experiments (Becker and Fuchs, 1969; Deubel, 1984; Ottes et al., 1984; Ottes et al., 1985; Coren and Hoenig, 1972) the peripheral target consists of two spots instead of one. If the spots are not too far apart, the saccade is aimed at a po­ sition somewhere in between. A 'centre of gravity' theory has been proposed to explain this phenomenon; however, positions closer to the fovea seem to have a higher weight than more ec­ centric positions (Findlay, 1982). These observations point to a mechanism that involves broadly tuned receptive fields. Pre­ cise control of saccades can be brought about by combining sev­ eral not finely tuned signals. The colliculus superior has been proposed as the location of this process (Mays and Sparks, 1981; Mcllwain, 1982; Ottes et al., 1985).

Similar to the averaging in position, the saccadic system also averages in time. If a target is displaced again during, or shorty before the primary reaction, the saccade lands some­ where between the first and the second position, provided that they are not too far apart. The transition between the two am­ plitudes is a consistent and continuous function of time. Two theories have been proposed to explain these results: an inte­ gration of position during a certain time window (Becker and Jurgens, 1979), and a low-pass filter followed by instantaneous sampling (Van Gisbergen et al., 1981).

The amplitude transfer function, or gain, of the saccadic system is not very rigid. Normally, the gain is around 0.9, causing most saccades to undershoot slightly, but it is very much dependent on the subject, the direction and several other stimulus conditions (Deubel et al., 1982; Henson, 1979; Jurgens et al., 1981; Prablanc and Jeannerod, 1975; Weber and Daroff, 1972). Furthermore, the gain can be changed very easily, either

-15-by optical means, or -15-by displacement of the stimulus during saccades. After a few minutes of training (or about 50-100 sac-cades) gain changes in the order of 0.2 can be accomplished easily. A decrease in gain is easier to achieve, however, than an increase. Adaptation is direction specific, but not ampli­ tude specific; if a subject is adapted using 10 deg steps, all saccades in the same direction will be influenced (Deubel, 1984; Deubel, 1986; Henson, 1978). This implies a system that is organized in several parallel direction channels. It seems that the plasticity of the saccadic system (as well as other eye movements) is caused by neurons in the cerebellum (Optican and Robinson, 1980).

The models of the saccadic system evolved mainly from Young's sampled data model (see Young (1981) for a review). In its simplest form it consisted of a sampler (every 0.2 sec), a dead zone, a delay, the eye muscle dynamics and visual feed­ back. The model has been modified later, in accordance with ex­ perimental findings, to include stochastic sampling, efference copy feedback and a more sophisticated 'dead zone'. Other modi­ fications involve the control of saccade shape (Van Gisbergen et al., 1981; JÜrgens et al., 1981), the separation of trigger­ ing and amplitude calculation (Becker and JÜrgens, 1979) and the proposition of several parallel direction specific gain adaptive channels (Deubel, 1984; Deubel, 1986).

2.3 The smooth pursuit system

Slow eye movements can be divided into three classes, de­ pending on the stimulus. A vestibular signal causes an opposite eye movement to counteract the retinal image displacement dur­ ing head or body movement, the vestibulo ocular reflex (VOR). The VOR is a relatively simple reflex, which is found in most species. Another compensating eye movement is the optokinetic nystagmus (OKN). OKN occurs when a large visual field moves continuously. Both reflexes consist of slow movements in the stimulus direction, interspaced with opposite saccades, giving the sawtooth nystagmus pattern. They can be suppressed only when a fixation target is available, which leads to the third type of slow movements, the smooth pursuit.

moving objects in a differently moving or stationary surround­ ing. In contrast to saccades, it requires a visual stimulus; without it, smooth pursuit movements are virtually impossible. Only a few subjects can learn to track an imaginary target, but only in the dark (Heywood, 1972). It is possible to some ex­ tent, however, to follow a perceptive movement, like alpha or sigma movement (Adler and Grüsser, 1981; Mack et al., 1982; Van der Steen et al., 1983; Wyatt and Pola, 1979).

The physiology of smooth pursuit is very complicated, and for a large part still unknown. The complexity is increased by the mixture of pursuit with the VOR and OKN systems. Several neural pathways exist, involving at least the cerebellar floc­ culus, the brain stem reticular formation and the cerebral hem­ ispheres. A review of many studies dealing with the neurology of smooth pursuit and other eye movements can be found in Leigh and Zee (1983).

An important feature of the smooth pursuit system is that it can make predictions; predictable movements are tracked without delay. Most of the research on smooth pursuit has been done with highly predictable periodic movements, usually sine waves. The gain of the system is close to unity for low fre­ quencies, with a sharp cutoff at 1.5 Hz. However, the cutoff frequency depends on the amplitude of the movement, meaning that the smooth pursuit system is not linear. In most models, the non-linearity is represented by a saturation velocity, al­ though this is not constant either but depends on time; higher velocities can be reached if the movement lasts longer (St.Cyr

b

and Fender, 1969 ; Lisberger et al., 1981).

In unpredictable situations, the smooth pursuit system usually reacts within 0.15 sec, which is faster than the sacca-dic system. It is difficult to measure the pursuit latency with continuously moving stimuli, because the extent of predictabil­ ity, and its influence on reaction time, will vary. Therefore, the latency is usually measured with a ramp, a stimulus that suddenly starts to move with constant velocity. In this case, a saccade will be used to catch up with the target, and smooth pursuit to follow it further. Because pursuit already starts before the saccade, some interesting experiments were possible with step/ramp stimuli, for instance, a step that moves the target in one direction, immediately followed by a constant

-17-velocity in the opposite direction (Rashbass, 1961). If the step is small, the eye can be seen to move in the direction of the stimulus velocity, although that increases the retinal er­ ror at that moment. These experiments have lead to the assump­ tion that the smooth pursuit system is a velocity servo system, with the aim of matching stimulus velocity, independent of ac­ tual retinal position. The matching is done rather roughly. Williams and Fender (1979) measured a 10% velocity mismatch with pure velocity stimuli.

However, a constant retinal error will evoke smooth pur­ suit movements as well. Experiments with eccentric afterimages (Heywood, 1972; Heywood and Churcher, 1971; Kommerell and Klein, 1971) and stabilized images (Wyatt and Pola, 1979; Wyatt and Pola, 1981) have proved this, although the relationship between retinal error and pursuit is very inconsistent, depend­ ing on many variables, like subject, motivation, and all kinds of target parameters (Pola and Wyatt, 1985; Tamminga, 1983). Therefore, most models of smooth pursuit ignore the position influence, and concentrate on the velocity.

In daily life, pursuit is usually brought about by a com­ bination of saccades and slow movements. The relationship be­ tween these two distinct types of eye movements is an intrigu­ ing topic. It seems that the two control mechanisms are, for the most part, independent, each responding in its own manner to target movements. However, saccades are sometimes suppressed when smooth pursuit is expected to catch up with the target, for instance in step/ramp situations (Rashbass, 1961). Furthermore, the smooth pursuit velocity is temporarily reduced if a saccade happens to be made during pursuit, but that effect is compensated by an increase (or decrease, if the saccade is opposite the smooth pursuit) in saccade amplitude, without changing the properties of the saccade (JÜrgens and Becker, 1975).

Because of the complexity of the neural ciruitry, many people have tried to describe the smooth pursuit system with a functional model. It usually consists of mathematically well defined simple operations, like differentiation, integration, addition, etc. Physiological data have been used as much as possible to enhance the probability of a correct description, but neural correlates are not always easy to find. Usually, the

main correlation between the neurology and the functional mod­ els is, that all functions, signals and connections in the mod­ el have been found physiologically. However, the neural net­ works are infinitely more complicated than any functional model can be. In spite of these limitations, a model can be very use­ ful for simulations, predictons, and in general to facilitate the understanding of the system.

Models of the smooth pursuit system have been published by many authors. A general picture which includes the characteris­ tics of the majority of the models is given in Fig 2.1. Note that Fig. 2.1 does not depict a new model, but the lowest com­ mon multiple of most existing models. Actual models consist of only some of the elements and pathways of Fig. 2.1. The figure is intended to clarify the relationships and common pathways of several models that have been presented in very different for­ mats in the literature. All models use the retinal position

(path G) or velocity (path A) to drive the oculomotor plant, and the eye, which in turn influences the retinal image. A neu­ ral representation of the oculomotor plant is sometimes includ­ ed in the 'efferent copy' path (F), in order to recreate an eye-velocity signal that matches the real velocity exactly. The integrators and differentiators cannot be ideal (time constants 0 and <°) if they represent neural circuits. But, to understand the models better, it is useful to consider them as ideal for the moment. Let us also assume that the velocity falls within the linear range of the saturation element B.

The simplest control loop would be GD, an integrating po­ sition servo system. It keeps the retinal error zero when the stimulus is not moving; at constant velocities, there will be a retinal error proportional to the stimulus velocity, and no ve­ locity error. There are some problems with this model: 1. The cutoff frequency is maximally 1 Hz, which is lower than meas­ ured (Becker and Klein, 1973). 2. Certain non-linearities are found in smooth pursuit, that are consistent only with a system that calculates the velocity; for instance, in the step/oppo­ site ramp experiments (Rashbass, 1961), it is impossible to explain the early start of smooth pursuit in the ramp direc­ tion. Also, saturation can be found in the velocity domain

b

(St.Cyr and Fender, 1969 ; Lisberger et al. 1981), and tachi-stoscopic presentation reduces smooth pursuit (Barnes and Hill,

-19-st+1

st+1

integrator differentiator

higher order input u

stimulus

position

<*0

(perceptive)

stimulus

velocity

-sT

delay

eye

position

retinal error saturation integrated velocity

velocity

>

central eye muscles integrator

retinal error

-<-visual feedback

Fig. 2.1: A compilation of different smooth pursuit models from the literature. The fig­ ure does not represent a new model, but the lowest common multiple of several models. The Laplace transform of the transfer function of the elements is given at the top.

1984). 3. Lastly, cells carrying velocity signals have been found in the smooth pursuit control loop (Noda et al., 1981).

An alternative solution to some of the problems is path ABCD, which has exactly the same properties in the linear range, but is now based on retinal error velocity (Bahill and McDonald, 1981). However, this model will not respond to steady retinal errors, if the differentiator (A) is not ideal. The smooth pursuit system does respond to stabilized eccentric tar­ gets (Wyatt and Pola, 1979) or afterimages (Kommerell and Klein, 1971). In fact, any model using only path A would face the same problem. A better frequency response can be reached for the integrating controller (C or G) if it is combined with a proportional one (E), as is proposed by Becker and Klein

(1973), (AB (C//E) D, where // means parallel with). With the proper choice of relative gains, such a system can have unity gain up to 2 or 3 Hz. A similar model, that likewise solves the problem of afterimage tracking is that of Barnes; it uses sim­ ple integrating position tracking G, parallel to the propor­ tional velocity tracking ABE (Barnes et al., 1978; Benson and Barnes, 1978; Barnes, 1982). From an engineering point of view, his model is probably the most efficient.

Some phenomena are still unexplained. First, there is the influence of prediction. Smooth pursuit is enhanced if the stimulus trajectory is predictable. Modelling the influence of predictability is extremely difficult. One method would be to insert a neural representation of the expected stimulus veloci­ ty somewhere in the system (Bahill and McDonald, 1981). Another phenomenon is the influence of attention on smooth pursuit. Barnes and Hill (1984) found that the influence of attention was simply an increase in gain, and that it did not change the other properties of the tracking. An interesting concept relat­ ed to these findings is the use of a copy of the efferent eye vel.ocity command (F), to create, with the retinal error veloci­ ty, a neural representation of the stimulus velocity. The ef-ference copy is clearly used in our perception of movement. Enhancement of this perception, by means of attention, and the

a,b influence of expectations (Kowler and Steinman, 1979 ) and predictions coming from higher centres, can be included logi­ cally at this point. The possibility to follow sigma movement

(Adler and Griisser, 1981; Behrens et al., 1985; Van der Steen

-21-et al., 1983) clearly indicates that perceptive movement can drive the smooth pursuit system, at least if the retinal infor­ mation does not contradict this perception (Mack et al., 1982).

b

Robinson (1971, Fig. 12 ) already proposed the scheme AB (E//F) D on the basis of the inconsistency of a high open loop

a,b

gain, a delay, and stability. Yasui and Young (1975 ) used the concept of stimulus velocity generation to explain the en­ hancement of vestibular nystagmus when an afterimage is pres­ ent, calling it perceptual feedback. Later, Lisberger et al. (1981) and Barnes and Hill (1984) used efference copy feedback. A different kind model, one that does not fit in the cat­ egory of system theory type models described before, has been proposed by Eckmiller (1981). His model is based on an inter­ nally generated eye velocity signal. His so-called 'velocity predictors' can be influenced by higher order processes, and are similar to the 'perceptual velocity signals' in the other models. The difference lies in the input from the retina. In Eckmiller's model a retinal error increases the velocity pre­ diction, thus causing an acceleration. If expressed in terms of the other models, this would mean elimination of the differen­ tiator in path A, further using path CD, in which higher order processes would play a role as well. An attractive feature of this model is that it can track a target with constant velocity with a zero position error, without explicitly involving 'pre­ diction', but it is not fully crystallized.

The summary and conclusion of this section is that a model that combines integrative position control (path GD) with pro­ portional velocity control (path ABED), a model that includes the influence of perceptual velocity via a copy of the efferent velocity command signal (F), as well as higher processes (H) is the logical candidate for a model that is able to explain all smooth pursuit characteristics in a consistent and simple man­ ner, although agreement has not yet been reached in the litera­ ture.

2.4 Fixation of a stationary target

Reducing the target velocity results gradually in a tran­ sition from smooth pursuit of moving objects to fixation of a stationary target. However, mainly due to experimental

prob-an prob-annulus (Steinmprob-an, 1965) or two dots (Bedell et al., 1984) is the target, but the number of microsaccades is smaller with those stimuli. However, the centre can be localized perceptual­ ly even better than it can be fixated (Bedell et al., 1984). Stimulus luminance does not affect fixaton (Steinman, 1965), but a change in colour moves the average fixation point slight­ ly, probably due to dispersion in combination with the misa­ lignment of the optical and visual axes of the eye (Fender, 1955).

Background movement influences the drift (Tamminga, 1983; Murphy et al., 1975), but does not degrade overall accuracy very much (the position standard deviation does not change). The type of fixational task seems to affect mainly the micro­ saccades, but does not influence the fixation accuracy either. Steinman et al. (1967) found that, with the instruction 'fix­ ate', subjects made more microsaccades than with the instruc­ tion 'keep your eyes steady'. High acuity visual (Bridgeman and Palca, 1980) or visuo-motor (Winterson and Collewijn, 1976) tasks result in fewer microsaccades during or just before car­ rying out the task.

Most research on fixation has been done with stabilized heads. Head movements do have a detrimental effect on fixation accuracy, though. If the head is not supported, the standard deviation of fixation increases 1.5-2 times, and the average drift velocity doubles (Skavenski et al., 1979). Larger head movements cause even larger retinal image movements (Steinman and Collewijn, 1980). The inadequacy of the vestibulo-ocular reflex, which normally counteract the head movements, is en­ tirely responsible for these effects.

The simplest way to account for the eye movements of fixa­ tion is to assume that they are the (noisy) remnants of the smooth pursuit and the voluntary saccade control systems. How­ ever, the observation that images that are stabilized on the retina fade fairly rapidly has raised the question of whether they could have some functional value, or could even be under (subconcious) control. Fading of retinal images occurs if there is not enough retinal movement. The amount and speed of fading depends on the stimulus contrast, the amount of movement, and the regularity of the movement. Flicker and periodic movements can sustain perception temporarily, but a stochastic movement

-24-lems, fixation has often been considered as a separate situa­ tion. An example of eye movements during fixation is given in Fig. 2 . 2 , which depicts a random movement in an area with 10-20 min arc diameter. The slow random drift (velocity less than 10-15 min arc per sec) is interrupted 1-2 times per second by a tiny saccade (5-10 min a r c ) . The numbers cited here are very individual; they a l s o vary from day to d a y , and depend on the stimulus.

The overall accuracy of fixation is not influenced very much by the form of the s t i m u l u s , as long as there is a clear real or imaginary fixation point available (Murphy et a l . , 1 9 7 4 ) . Fixation degrades very little if the imaginary centre of

U L

a

d-E ™

>

X (min arc)

^ 2

c

c T

o

r^^^i

\r

Time (sec)

Fig. 2 . 2 : Example of normal eye movements during fixation of a stationary target; lower p a n e l : as a function of t i m e ; upper p a n e l : as a position p l o t .

is needed for a comlete suppression of fading. The best for continuous perception seems to be a movement pattern that looks like fixational eye movements, however with a larger amplitude, at least for para-foveal images (Gerrits and Vendrik, 1974). Larger movements are necessary for keeping continuous hue per­ ception (Ditchburn and Foley-Fisher, 1985). Also, fading occurs more rapidly if eye movements that do not correlate with reti­ nal image movements are made (Coren and Porac, 1974). In gener­ al, it seems that fixational eye movements are very functional in preventing fading by stabilization, and could be the result of an active optimization process.

During normal life, however, with binocular vision of high and median contrast images, and a considerable amount of head movements, fixation is never as good as in a laboratory experi­ ment, and fading never occurs. Together with the finding that eye movements do not increase with high acuity tasks, this sug­ gests that fixational eye movements are not actively generated

in the process of keeping optimal vision (Kowler and Steinman, (1980); Steinman et al., (1973).

If this is true, eye movements during fixation can be con­ sidered as physiological noise, filtered by the fixational con­ trol systems. Both microsaccades and slow movements are noisy and are not always directed towards the centre of fixation. The question as to which one of the two contributes most to a steady gaze, and as to whether they are related to voluntary. saccades and smooth pursuit has intrigued many scientists.

The slow movements look random, and have obviously often been considered as noise, imbalance of the eye muscles, or of higher centres, and were often called 'drifts' (Ditchburn, 1980; Ginsborg, 1953). Cornsweet (1956) did not find any corre­ lation between distance from overall mean position and the drift velocity during 0.5 sec periods afterwards. He also sta­ bilized the image, and did not see an increase in drift veloci­ ty. Both measurements are in agreement with the apparently ran­ dom character of drift. Later, however, Nachmias (1959) found a slight negative correlation between drift velocity and position in some directions, being the directions in which saccades did not correct very well (a negative correlation means a movement a that decreases the retinal error). St Cyr and Fender (1969 ) also found that most 'drifts' decreased the retinal error

-25-what. Furthermore, drift increases in the dark, in contradic­ tion with the random hypothesis. The question of whether slow movements alone could keep the eye in place was settled when Steinman et al. (1967) found that it was not difficult to learn to suppress microsaccades using simple verbal feedback, and that, if subjects succeed in doing so, they could then keep their eyes fixated just as well. This has been checked by oth­ ers (Steinman et al., 1973; Murphy et al., 1975; Kowler and Steinman, 1980). However, subjects who can suppress microsac­ cades do report that they have to look at the stimulus differ­ ently, more in line with the instruction 'keep your eyes fixed' than 'fixate, the stimulus'. Thus, the question of whether 'slow control' plays a role when microsaccades are also present has not been solved. A relationship between slow control and smooth pursuit has been suggested (Nachmias, 1959; Murphy et al., 1975), but never tested. Obviously, a model for smooth pursuit that works as a fixation control system must be a position con­ trol model (path G in Fig. 2.1).

In the older literature, microsaccades were considered as automatic and involuntary. Indeed, without training, they occur unconsciously and unnoticed. Microsaccades seem to be triggered by a retinal error, as the chance of a saccade increases rapid­ ly with the error (Cornsweet, 1956). Cornsweet also found that the saccade rate decreased when the image was stabilized. How­ ever, Nachmias (1959) concluded that the time since the last saccade was a better predictor for the chance of a saccade than the retinal error. He also observed that saccades were usually directed towards the centre of fixation, but often missed the

a

target. St. Cyr and Fender (1969 ) concluded that saccades were on the average corrective, but inaccurate.

In contrast with this hypothesis of an automatic control system is the notion that microsaccades can be suppressed and made voluntary (Haddad and Steinman, 1973), without much train­ ing. If they are suppressed, fixation is not affected signifi­ cantly. If saccades can be made voluntary, and are not needed for good fixation, why should we normally make them, Kowler and Steinman (1980) asked. Other foveate animals like cat and mon­ key do not usually make them either (Winterson and Robinson, 1975). Kowler and Steinman (1980) suggested that they do not have any functional value, and are laboratory biteboard

arti-facts of people that read too much. However, most people do make microsaccades automatically under these standard condi­ tions, and microsaccades have control properties, as is proven in the older literature.

Therefore, it is interesting to see their relationship with larger, visually triggered saccades. Dynamically, micro­ saccades are similar to their larger counterparts. They have the same amplitude-velocity-duration characteristics (Zuber and Stark, 1965). They cause the same contrast threshold elevation

(Zuber et al., 1964). They are triggered by a retinal error, a,b

just as larger saccades are (Wyman and Steinman, 1973 ; Nach-mias, 1959). The saccade precision (standard deviation) de­ creases smoothly from larger saccades down to microsaccades

(Timberlake et al., 1972). The same burst cells in the reticu-lar formation generate macro- and microsaccades in a simireticu-lar fashion (Van Gisbergen and Robinson, 1977). In conclusion, mi­ crosaccades during fixation do not seem to differ from larger saccades. They are just as voluntary as breathing, and their occurrence can be influenced under conscious or subconscious control.

-27-3. METHODS

3.1 Introduction

Several techniques have been applied in the past for the measurement of eye movements. A fairly extensive review has been given by Young and Sheena (1975), and, more recently, by Robinson (1981). All methods have been improved in reliability and resolution since then, but have not changed dramatically. The electro oculogram, which is widely used, especially in clinical environments, measures the moving dipole of the eye with electrodes attached to the skin. The method is rather in­ accurate, and unstable. The resolution is usually not better than 1-2 deg. In several optical techniques either the limbus boundary (resolution 0.5-2 deg) or the reflection from the cor­ nea (resolution 0.5-1 deg) has been used, usually with infra­ red light. The corneal reflection is sometimes combined with the centre of the pupil, to aquire suppression of head movement artefacts. A very sophisticated method combines the corneal re­ flection (first Purkinje image) with the reflection from the rear lens surface (fourth Purkinje image), to achieve both head movement compensation and a high resolution (about 1 min arc; Crane and Steele, 1978). The method, however, is very expen­ sive, and requires considerable skill to operate and maintain.

With the possible exception of the double Purkinje image eye tracker, none of these methods is accurate enough for the measurement of fixational eye movements, in which an resolution of at least 0.5 min arc is needed (see section 2.3). In another category of methods attachments to the eye are used, usually tightly fitted contact lenses. Mounted on the lens is a mirror, lamp or radiant spot, or a coil. At the price of some discom­ fort, these systems provide very high resolution (in the order of 0.1 min arc) and a good accuracy, if the contact lens does not slip. The optical methods (mirror, radiant spot tracking) require a conversion from the optical to an electrical signal that can be processed further. They also need special individu­ ally fitted contact lenses, sometimes held in place by suction. The magnetic 'search coil' method provides a direct electrical signal, and does not need fitted lenses. Therefore, and because

-29-of the simplicity and the reliability -29-of the method, we chose the search coil magnetic system.

3.2 Eye movement recording with a coil in a magnetic field

First suggested by Robinson (1963), the method is based on the voltage that is induced in a coil, placed in an alternating magnetic field. If the field can be described as H coswt, then

x the induced voltage in a coil will be

U =NAH wsinutsina i x

where N is the number of turns and A the area of the coil, a is the angle between the field direction and the plane of the coil. For small angles, the amplitude of the induced voltage is proportional to a. Translation of the coil does not change the voltage if the magnetic field is homogeneous.

The coil is mounted in a silicon rubber contact annulus, developed by Collewijn et al. (1975); it is commercially avail­ able. The annulus fits around the iris of the eye, and is held in place both by suction (its curvature is greater than the eye's) and by the cornea that bulges through the opening of the annulus. The thin copper lead leaves the coil at the nasal side (except for one subject (JS), who found the temporal side more convenient) and passes through two adjustable stationary offset correction coils to a transformer. The transformer is both a safety measure and an adaptation of the low coil impedance to the lock-in amplifier that measures the ampltitude of the coil voltage, synchronized with the field frequency, and filters the resulting dc-signal with a second order low pass filter (time constant 3 m s ) . The signal is then sampled at 100 Hz, read by a DEC LSI-11/02 micro computer, and usually stored on disc for analysis. By using another, vertical field, oscillating at a different frequency, and another lock-in amplifier, both hori­ zontal and vertical rotations can be measured simultaneously. The system's resolution is 0.1 min arc (st.dev. of noise level).

The magnetic fields were generated by two large square coil pairs, placed in a cube around the subject. The size of the coils determines the homogeneity of the field in the

STELLINGEN

behorend bij het proefschrift:

The control properties of small eye movements.

1 . Een probleemloze methode om oogbewegingen te meten bestaat niet.

2. Het onderzoek naar de regeling van fixatie van een stil­ staand object is alleen vruchtbaar als het object beweegt.

3. Alleen al het feit dat een discussie over de relatieve be­ langrijkheid van microsaccades en langzame bewegingen bij fixatie mogelijk is, toont aan dat beide typen oogbewegingen stuureigenschappen bezitten.

4. Oogbewegingen van baby's bij fixatie lijken verrassend veel op die van volwassenen, als voor "boogminuten" wordt inge­ vuld "booggraden".

5. De beschrijving van de visuele contrastgevoeligheid in ter­ men van Fourier-getransformeerden heeft bijzonder veel nut gehad, juist door haar controversiële karakter; het model heeft een lawine van experimenten uitgelokt die onze kennis van het visuele systeem enorm hebben vergroot. Tegelijk heb­ ben echter die experimenten de tekortkomingen van het model aangetoond.

6. Het grote adaptieve vermogen van onze visuele perceptie blijkt onder andere uit het feit dat wij vlakke, contrastar-me, stilstaande, onscherpe, zwart-wit afbeeldingen (zoals krantefoto's) beschouwen als afspiegelingen van de werke­ lijkheid.

7. Al ziende leert men zien.

8. Natuurkundigen die een psychofysisch onderzoek verrichten dienen goede nota te nemen van de experimentele psychologie.

9. Nu de uitkomsten van medische onderzoeken steeds meer kwan­ titatief zijn, zou de computer een grotere rol kunnen spelen bij de diagnostiek van ziekten dan tot nu toe. De betekenis van veel onderzoekuitkomsten voor een diagnose is echter nog te weinig kwantitatief vastgelegd.

10. Veel macro-economische regelsystemen zijn instabiel door een te grote vertraging in de regelkring. Het Europees landbouw­ beleid is hiervan een goed voorbeeld.

11. Gelijkwaardige kruisingen passen niet meer in het huidige verkeerspatroon, en dienen te worden afgeschaft.

12. Een brede stadsbus met de uitlaat rechtsachter is ontworpen door iemand die weinig fietst.

centre, where the eye is positioned. The coils were, along with a series capacitor, part of an oscillating circuit. The ampli­ tude of the field was kept constant by the electronic circuit of Fig. 3.1.

The design criteria of the fields were as follows. The criterion for the size was the uniformity of the field. Coils of 1 by 1 m were chosen, giving an error less than 0.5% in an area of 8x8x8 cm in the centre. More details on the field cal­ culations are given in the next section. Since the induced vol­ tage is proportional to the field frequency, a high frequency was chosen. On the other hand, the frequency was limited by the electronics and the coil resistance. As a compromise, 17 and 23 kHz were chosen, just above the audio range. Each coil consist­ ed of one hundred turns, plus one for feedback. The resulting field H at the centre between the coils was about 2 A/m.

x

3.3 The field uniformity.

The error that is due to head translations depends on the uniformity of the magnetic field. In the following section we will only describe the errors caused by deviations of the hor­ izontal field. Similar errors exist, of course, for the verti­ cal field. Let us call the axis through the centres of the field coils x, the primary visual axis of the subject in the field z, and the vertical axis y. The centre of the coordinate system will be the midpoint between the coils. The horizontal field at the centre is directed along the x-axis, and will be called HQ. On the x-axis, away from the centre, the field am­

plitude changes, but not its direction, due to the configura­ tion symmetry. A similar amplitude change occurs if we move away from the centre in the plane x=0. Since the output of the search coil is proportional to H as well as to the angle of

x

the plane of the coil with the x-axis (the variable we want to measure), it is clear that a change in H causes a relative

x

error, a change in the gain of the system. The relative gain error n=H /H will be used to express the influence of this

x change.

Away from the plane x=0, and off the x-axis, the direction of the field changes as well as the amplitude, in other words, H and H are no longer zero. Due to the symmetry, H will be

our

F/flD RF&ULflTOR

1

"^?--

-CD-^«toO? ef>9£>#4A/T HtHT'ft/ff

Fig. 3.1: Electronic circuitry for the field amplitude regulator. The input is provided by a stationary pick-up coil. The signal is amplified, rectified and compared with a reference. The difference with the reference voltage is then multiplied by the parallel positive feedback; after a phase shift and amplification it is fed back into the coils and a series capacitor, closing the oscillating loop.

of the same order of magnitude as H . Their influence on the y

output of the search coil is different, however. If the search coil plane is perpendicular to the z-axis (the subject is look­ ing straight ahead), H will not induce a voltage in the coil.

y

Only when the search coil rotates will H cause a cross-talk y

between vertical and horizontal rotations, but it is small com­ pared to the influence of H , as long as the deviation from the

z

primary axis is small (within about 20 deg).

H is perpendicular to the search coil when the eye is z

looking in the primary direction, thus will induce a voltage that changes only slightly when the eye rotates, as long as the rotation is within about 20 deg. Therefore, H will cause an

. z offset error e=H /H radians. Since H must be of the same

or-z or-z der of magnitude as the change in H (the primary field), the

x

offset error can be of relatively large importance for eye movement measurements, specially if the search coil is not per­ fectly centred between the field coils, as is the case in bi­ nocular measurements. However, the offset error has not been recognized properly in the eye movement literature.

Robinson (1963) calculated the gain error in his coil pair design, in which the distance between the coils 2d is twice their radius rQ:

gain error n = (1.125x2 - 0.563z2)/rn2

R °

offset error e = 1.125xz/r02 (for r0=d, y=0) R

The influence of y is similar to that of x, and is left out here for reasons of simplicity. Plots of constant error are

b

given in Fig. 3.2 . Note that the gain error is expressed in %, and the offset error in min arc. Although only the Robinson pair is used in the measurement of eye movements, is commer­ cially available, and is used by us as well, it is not the op­ timal pair for field uniformity. That privilege belongs to the Helmholtz pair, with an inter-coil distance 2d equal to the radius r0. In the Helmholtz pair, the second order field error

vanishes, leaving the fourth order as the most important error component. In the Helmholtz pair the errors are:

Circular coils, d=0.5

Circular coils. d=l

a ' ' ' ' ' o i i i i

0.00 0.20 0.40 0.00 0. 10 0.20

Primary axis (Z) Primary axis (Z)

Fig. 3.2: Lines of constant error in the magnetic field with circular coils. Solid curves represent gain errors of 0.25, 1 and 4 %. Dotted curves are offset errors of 1, 4 and 16 min arc. Only one quad­ rant is plotted, with the centre of symmetry at the origin, a: Helmholtz configuration, b: Robinson con­ figuration. The scale is expressed as a fraction of the coil radius; note the difference in scale between the two figures.

gain error n = (-1.152x* + 3.456x2z2 - 0.432z")/r„*

H

offset error e = (-2.304x3z + 1 .728xz3)IT." (r =2d,y=0)

H °

(see the Appendix for detailed calculations). A constant error plot makes it clear that it differs substantially from the

a

Robinson design (Fig 3.2 ) . Note the different scale.

It is obvious that for binocular measurements, or experi­ ments with free head movements, the classical Helmholtz design is preferable. The free field of view, however, is only 45 deg in t.he Helmholtz pair, compared to 90 deg in the Robinson pair. In our own measurements, with a fixated head, properly aligned in the centre of the field, a conventional Robinson design has been used. The offset error due to a head movement of 3 mm was less than 0.1 min arc, negligable compared with other sources of error. For the square coils that we have used, the error is about 10% smaller than for circular coils. Let 2a be the length of an edge; then:

-34-ri = (0.833x2 - 0.417z2)/a2

e = 0.833xz/a2 (a=d, y=0)

The optimal distance 2d between square coils is d=0.5445a. The remaining errors in that situation are again of the fourth or­ der, similar to the ones caused by circular coils, but about 10% smaller. Equal error plots for both square coil pairs are plotted in Fig. 3.3. Calculations of the field strength and the errors are presented in the appendix.

Square coils, d=0.545

Square coils, d=l

i 1 - | — — I i 0. 00 0. 20 0. 40

Primary axis (Z)

o. oo o.

o. 20

Primary axis (Z)

Fig. 3.3: Lines of constant error in the magnetic field with square coils. Solid curves: gain errors of 0.25, 1 and 4 %. Dotted curves: offset errors of 1 , 4 and 16 min arc. Only one quadrant is plotted, a: Op­ timal configuration, b: Usual configuration (cube). The scale is expressed as a fraction of half the side of a coil.

3.4 Accuracy of the eye movement recording

3.4.1 Introduction

In the search coil method, with the head properly stabi­ lized, the accuracy is limited by the calibration accuracy and displacements of the contact annulus on the eye. Inspection of

the fixation records revealed that there were no sudden large displacements. However, during the course of an experiment

(lasting about 30 min) a slow drift sometimes occurred. Fig. 3.4 shows some typical results of repeated calibration measure­ ments during an experimental session. The total displacement can be in the order of 30 min arc when an annulus is placed asymmetrically on the eye. This means that an absolute position calibration must come from the fixation records themselves. The limit of absolute calibration, however, is the accuracy of fix­ ation (st.dev. 2-5 min arc). Smaller contact annulus displace­ ments during a single trial cannot be detected from inspection of the records. Displacements of this magnitude can affect the results seriously if fixational eye movements are studied in detail, or if the retinal image has to be stabilized.

L a a d a C <=> O ó-\ —H C\J •P ■r-l w ■

o

>

<

x

x

Trial numbgr

Fig. 3.4: Repeated offset calibration during an ex­ periment. Each symbol represents the average eye po­ sition (x and y) during 10 sec. The time between suc­ cessive calibrations was about 50 sec.

In the past, a number of objective precision measurements have been carried out, for instance by Byford (1962), Barlow (1963) and Riggs and Schick (1968). They were mainly concerned

-36-with contact lens slippage. Byford (1962) used a number of techniques, including the observation of a tiny piece of ciga­ rette paper attached to the eye, and concluded that slip was less than 1 min arc for normal fixation eye movements. His methods, however, were very laborious.

Barlow (1963) developed an afterimage technique, and con­ centrated his research on devices used for stabilizing the ret­ inal image. He developed the idea of applying a Vernier acuity technique to judge the difference between an afterimage and a stabilized image, but he used this method only qualitatively. His quantitative measurements concerned a Vernier offset be­ tween two afterimages that were applied via the stabilizing de­ vice, with an interval time of 5-10 seconds. Barlow concluded that the Yarbus-type eye cups (mean displacement 0.7 min arc) were better than scleral fitting lenses (3 min arc).

Riggs and Schick (1968) developed Barlow's idea of compar­ ing an afterimage and a stabilized image. Subjects saw one half of a line as an afterimage, and the other half as a stabilized image; both were kept visible by periodic interruption of the background light. They could move the stabilized half across the retina with a control knob, which they used to keep the two halves aligned. The output of the control knob thus gave a con­ tinuous record of stabilized image displacements. Riggs and Schick achieved accuracies better than 0.5 min arc with their light limbus fitting contact lenses.

The method of testing used by Riggs and Schick (1968) seems to be superior, but has some disadvantages. A stabilized image of a line is needed, which is not always easily availa­ ble. Also, the subject has to compare a stabilized image and an afterimage, which might be difficult, because the latter tends to fade or change in sharpness, and might look very different from the stabilized image.

3.4.2 Method

We did not use stabilized images in our procedure, thus making the method applicable to all eye movement measuring de­ vices. Instead, we used two afterimages with a Vernier offset

(like Barlow (1963) did). We produced bright exposures of the upper half and the lower half of a vertical slit, some time

interval apart, while the subject fixated an LED located in the centre of the slit. The exposures were made by two simple pho­ tographic flash units, in an arrangement like Fig. 3.5. The distance from the subject was 4.3 m, and the slit dimensions 2 by 40 min arc. If the subject's gaze direction during the sec­ ond flash is not exactly the same as during the first, a Verni­ er offset can be observed in the afterimage. To enhance the visibility of this afterimage, we used a flickering field (fre­ quency 1-5 Hz ) .

40 MIN.

OF ARC

i-< 2 MIN. OF ARC

2 LED

B

Fig. 3.5: Arrangement for producing two afterimages with a Vernier offset. A: rear view. B: View from the subject's position.

Normally, due to fixational eye movements, a Vernier off­ set can be seen, when the two flashes are a few seconds apart in time, even with steady fixation. At the time of the two flashes (within 200 microseconds) we measured the horizontal eye position. Then we compared the subject's judgement of the Vernier offset with the difference between the measured eye positions.

We used this procedure to test our method of measuring eye movements using the search coil. The method is generally be­ lieved to be one of the most reliable currently available, and its use is widespread. The major disadvantages of the method

-38-are a restricted measurement time (maximally 40 minutes), and the effect that the annulus sometimes has on visual acuity (see Arend and Skavenski, 1979). Often, vision can be improved by repeated blinks, but occasionally the image remains blurred or double.

The subject gave only the direction of the Vernier offset, not an estimation of its size, for three reasons:

1. Vernier offset sizes tend to be overestimated.

2. The threshold for size increments is higher than the thres­ hold for detection of the Vernier step.

3. The two afterimages are not exactly the same: sometimes there is blur because of accomodation changes or tear fluid. Also, one afterimage is a few seconds older than the other and therefore different in appearance. Judgements on the Vernier offset sign are less sensitive to these differences than size judgements are.

Correct trials were those in which the subject's judgement cor­ responded to the measured eye position difference. Fig. 3.6 shows an example of a histogram of incorrect responses, as a function of the measured position difference. There are two ways to obtain such a histogram. The simplest way is just to repeat trials with a fixed interflash interval. The normal fix­ ation eye movements will cause a distribution of position dif­ ferences with a standard deviation of 2-5 min arc. However, many trials could be wasted by this method, because the subject will always be correct with large differences, if the eye move­ ment monitor is accurate enough. Another method is to vary the time between flashes (within limits), and give the second flash only at a time when the measured position difference is smaller than a desired value. The latter procedure was used in our ex­ periment: The eye position was sampled every 0.2 sec, and the second flash was applied only if the difference with the first position was within a certain limit. The limit was varied be­ tween sessions in order to obtain a sufficient number of sam­ ples in the relevant part of the distribution curve. The vari­ ance that can be calculated from the distribution of incorrect responses is the sum of the afterimage Vernier acuity and the 'noise' of the eye movement monitor. The sensitivity of the method is restricted by the afterimage Vernier acuity, about 0.1-0.3 min arc, depending on the experimental conditions.

CO u. _i

o <

5

uj

20-o 20-o:

cr o:

0-HORIZONTAL

/32

/

u*

_C

₎

3/

/31

'31

I

2

VERTICAL

40'

20-1

^i

0

j)

32

^ h e

2

POSITION DIFFERENCE (MIN. OF ARC)

Fig. 3.6: Histograms of the number of psychophysical responses that were different from eye position meas­ urements. The ratio between the number of different responses and the total number of trials is indicated above the bars.

This method will detect all errors in the eye movement monitor that are present during either one of the flashes. It will pick up noise in the measuring device itself, contact lens displacements or head movement artefacts. It cannot detect dy­ namic errors like contact lens lag during saccades, or a very slow drift. The influence of blinks, large eye movements or head movements can be studied by instructing the subjects to make these movements in between the first and the second flash.

3.4.3 Results

The results of the experiment we conducted to test the precision of the coil/annulus method have been plotted in Fig. 3.6, for horizontal and vertical orientations of the Vernier step. The interval between the flashes has been varied between 5 and 10 sec. Subjects were instructed to keep fixating the LED, and to ignore the flashes. Sometimes, reflex blinks and eye movements caused by the flash were difficult to suppress, however. The standard deviations have been calculated from the histograms using probit analysis (Finney, 1971), and are 0.9 min arc for horizontal movements and 1 .0 min arc in the verti­ cal direction. Vision in some of the sessions had been affected

-40-to an extent that would have led -40-to rejection of the data in normal eye movement experiments. We included these data in the present results, however, so that these represent worst case conditions. Being interested mainly in using the eye movement monitor for the study of steady fixation, we did not extensive­ ly measure the effect of saccades on the precision of the sys­ tem. We performed some pilot studies, which did not show any effect of saccades up to 10 degrees. Blinks can displace the annulus, though. Regularly, we found displacements in the order of 2 min arc. If absolute position information is critical, it seems advisable not to make blinks within trials. Our conclu­ sion is that, apart from blinking effects, the Robinson / Col-lewijn method of measuring eye movements has a precision better than 1 min arc.

Summarizing, the above-described method of testing eye movement measuring equipment is simple, economic and accurate. It makes image stabilizing devices unnecessary, and it can be used when vision is relatively poor, because poor vision has little effect on Vernier acuity. A disadvantage is that it takes a long time to measure a complete distribution curve. Each pair of flashes gives only one trial, and the time between trials is 1-2 minutes, because the afterimage has to fade suf­ ficiently before the next flash pair can be applied. Fading also limits the inter-flash time, making the method suitable only for short-term stability, with a maximum of about 60 sec when using very strong flashes.

3.5 Stimuli, subjects and experimental procedures

Except for one experiment, in which a Landolt-C was pro­ jected by a modified slide projector, all stimuli were generat­ ed under computer control on a good quality black and white TV-monitor. The decay time constant of the monitor phosphor was 20 ms, and it was operated at 50 Hz. Stimuli were usually small bright dots or line segments in a dark surrounding, with the brightness kept at about 2 log units above foveal threshold. Stimulus flicker was not perceived under those conditions. Screen resolution was 0.63 mm horizontal and 0.44 mm vertical (2.15 x 1.51 mih arc at 1 m distance). Distance from the screen was varied between 1 m (for saccade experiments) and 10 m (for

pure fixation experiments). Screen size was 512 x 512 pixels (18 x 13 deg at 1 m ) . In some experiments, the image of the stimulus was stabilized on the subject's retina, by using the sampled eye positions to control the stimulus position on the screen. In these experiments, the eye movement recording was synchronized with the TV-generator, and the image was updated during the vertical blanking period, to prevent irregular flickering because of interference. Fading of the image because of the stabilization occurred, but was interrupted by each sac-cade, due to the unavoidable 20 ms time lag of the screen up­ date.

The author, colleagues and university students served as subjects. Some were completely naive, and served for the first time as subjects in eye movement research. The only criterion for the selection of subjects was a good monocular visual acui­ ty with the proper optical corrections. Only one subject was rejected due to irritations caused by the annulus. Some sub­ jects used their right eye and others the left, based mainly on the refractional error of the eye.

An experiment went as follows: First the eye was anaes­ thetized locally with one or two drops of Novesine 0.4% (oxybu-procaine hydrochloride). The anaesthetic does not interfere with vision, and wears off in about 15 min. The contact annulus was wetted with Ringers solution, the upper eyelid pulled up­ ward, the annulus slid underneath and then the lower lid was pulled over the annulus. The subject was then asked to blink a couple of times, to let the annulus settle symmetrically around the iris. Then the subject closed his/her eye, and the annulus was pressed on firmly through the eyelids. This way of applying the search coil was much friendlier to the subject than when the common application tool (Collewijn et al., 1975) was used. The other eye was then closed and taped. We found that closing and taping the eye was more comfortable than covering it with an eye patch,• ancl often prevented blinking. The subject was aligned at the center of the field coils with the head fixed in a biteboard, headrest and sometimes supports at the sides of the head.

An experiment always started with a calibration, which was repeated once or twice during the experiment. For the purpose of calibration, the subject was instructed to follow a target

-42-that jumped to four corners of a square, and stayed at each corner for 3 sec. The order of the target jumps was randomized, and the eye position averaged for a 1.5 sec period, ending 0.5 sec before the next jump, to prevent any influence of expecta­ tions on the eye position (Kowler et al., 1984; Kowler and

a ,b

Steinman, 1979 ) . Calibration trials with blinks were dis­ carded. A calibration sequence was repeated four times, hori­ zontal and vertical scale factors calculated separately from each sequence, and averaged afterwards. The size of the cali­ bration square varied between 1 and 8 deg, depending on the experiment. The accuracy of gain calibration was always better than 1%.

After the calibration, the subject started each trial when ready. A trial lasted between 5 and 20 sec usually. The subject reported the amount of image blur during or after the experi­ ment, and it was repeated if the blur was expected to have in­ fluenced the results. Two types of 'blur' were reported: double or multiple images, and a milky haze throughout the visual field. The latter lasted until some minutes after the experi­ ment. The coil was removed from the eye by letting the subject look upwards, inserting the lower eye lid under the coil, and letting the subject look downwards while holding the upper lid. The whole experiment never lasted longer than 40 min.

*

These results have been published in Vision Research (De Bie, 1985).